K-theory for ring C*-algebras attached to function fields

TL;DR

This paper calculates the K-theory of ring C*-algebras associated with polynomial rings over finite fields, revealing structural similarities with number field cases and providing explicit generators through a duality theorem.

Contribution

It introduces a duality theorem for these algebras and explicitly determines their K-theory and generators, highlighting parallels with number field scenarios.

Findings

K-theory of ring C*-algebras for polynomial rings over finite fields is computed.

The K-theory possesses a ring structure with explicit generators.

Striking similarities between the number field and function field cases are established.

Abstract

We compute the K-theory of ring C*-algebras for polynomial rings over finite fields. The key ingredient is a duality theorem which we had obtained in a previous paper. It allows us to show that the K-theory of these algebras has a ring structure and to determine explicit generators. Our main result also reveals striking similarities between the number field case and the function field case.